reserve A for QC-alphabet;
reserve p, q, r, s, t for Element of CQC-WFF(A);
reserve X for Subset of CQC-WFF(A);

theorem
  'not' p => 'not' q is valid iff q => p is valid
proof
  thus 'not' p => 'not' q is valid implies q => p is valid
  proof
    assume
A1: 'not' p => 'not' q is valid;
    ('not' p => 'not' q) => (q => p) is valid;
    hence thesis by A1,CQC_THE1:65;
  end;
  assume
A2: q => p is valid;
  (q => p) => ('not' p => 'not' q) is valid;
  hence thesis by A2,CQC_THE1:65;
end;
